As told or recounted rather than shown. Derived from diagesis, a style of fiction. In diagesis, a narrator tells a story. It has stood in contrast with mimesis -- in which you are shown rather than told -- since Aristotelean times.
When Jack Johnson sings about the diagetic world, he is talking about the world you are told about, and complaining that you can't accept the narrative that you hear.
Alternately, one can think of the Director's cut of Blade Runner as more mimetic, forcing you to put things together, while the one that was put in theatres with the voice overs to fill in the gaps as a more diagetic presentation.
This word is probably a bit uppity for this place, but it doesn't appear in the dictionary, and two incorrect definitions have already been given.
You can't believe everything you hear
The DIAGETIC world is so unclear
So baby close your ears
On the news tonight